One of the fundamental reasons for the hysteretic nonlinear behavior of porous reservoir media is that heterogeneous or damaged materials contain an enormous number of mesoscopic features such as microcracks and macrocracks, joints, and grain to grain contacts containing multiphase liquids. Each of these mesoscopic units exhibits a hysteretic behavior which dominates the macroscopic reservoir response. Fluids in the reservoir may significantly influence the quasistatic and dynamic response in porous materials of the reservoir media due to the activation of internal molecular forces. Hysteresis can affect oil recovery efficiency because of the induced relative permeability reduction and the associated trapping of oil.